Publications

• Refereed Journal Publications
  
  
  • 19) S. Yakovlev, L. Xu, and F. Li, Locally divergence-free central discontinuous Galerkin methods for ideal MHD equations, submitted, November 2011.
  
  
  • 18) F. Li and L. Xu, Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations, [PDF], Journal of Computational Physics, DOI: 10.1016/j.jcp.2011.12.016, v231 (2012), pp.2655-2675.
  
  
  • 17) F. Li, On the negative-order norm accuracy of a local-structure-preserving LDG method, [PDF], Journal of Scientific Computing, DOI: 10.1007/s10915-011-9503-5, in press, 2011.
  
  
  • 16) F. Li, L. Xu and S. Yakovlev, Central discontinuous Galerkin methods for ideal MHD equations with the exactly divergence-free magnetic field, [PDF], Journal of Computational Physics, DOI:10.1016/j.jcp.2011.03.006, v230 (2011), pp.4828-4847. (Correction: in section 4.2.6, it is `with the darker area representing the smaller value).
  
  
  • 15) W. Guo, F. Li and J. Qiu, Local-structure-preserving discontinuous Galerkin methods with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations, [PDF], Journal of Scientific Computing, DOI: 10.1007/s10915-010-9434-6, v47 (2011), pp.239-257.
  
  
  • 14) Y.-T. Zhang, S. Chen, F. Li, H.-K. Zhao and C.-W. Shu, Uniformly accurate discontinuous Galerkin fast sweeping methods for Eikonal equations, [PDF], SIAM Journal on Scientific Computing, DOI: 10.1137/090770291, v33 (2011), pp.1873-1896.
  
  
  • 13) B. Cockburn, J. Gopalakrishnan, F. Li, N.-C. Nguyen, and J. Peraire, Hybridization and postprocessing techniques for mixed eigenfunctions, [PDF] , SIAM Journal on Numerical Analysis, DOI: 10.1137/090765894, v48 (2010), pp.857-881.
  
  
  • 12) F. Li and S. Yakovlev, A central discontinuous Galerkin method for Hamilton-Jacobi equations, [PDF], Journal of Scientific Computing, DOI: 10.1007/s10915-009-9340-y, v45 (2010), pp.404-428. (Special issue in memory of Professor David Gottlieb)
  
  
  • 11) S. C. Brenner, F. Li and L.-Y. Sung, Nonconforming Maxwell eigensolvers, [PDF], Journal of Scientific Computing, v40 (2009), pp.51-85.
  
  
  • 10) S. C. Brenner, F. Li and L.-Y. Sung, A nonconforming penalty method for a two-dimensional curl-curl problem, [PDF], Mathematical Models and Methods in Applied Mathematics, v19 (2009), pp.651-668.
  
  
  • 9) F. Li, C.-W. Shu, Y.-T. Zhang and H.-K. Zhao, A second order DGM based fast sweeping method for Eikonal equations, [PDF] Journal of Computational Physics, DOI: 10.1016/j.jcp.2008.05.018, v227 (2008), pp.8191-8208.
  
  
  • 8) S. C. Brenner, J. Cui, F. Li and L.-Y. Sung, A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem, [PDF]  Numerische Mathematik, v109 (2008), pp.509-533.
  
  
  • 7) S. C. Brenner, F. Li and L.-Y. Sung, A locally divergence-free interior penalty method for two-dimensional curl-curl problems, [PDF]  SIAM Journal on Numerical Analysis, v46 (2008), pp.1190-1211.
  
  
  • 6) S. C. Brenner, F. Li and L.-Y. Sung, A locally divergence-free nonconforming finite element method for the reduced time-harmonic Maxwell equations, [PDF]  Mathematics of Computation, v76 (2007), pp.573-595.
  
  
  • 5) F. Li and C.-W. Shu, A local-structure-preserving local discontinuous Galerkin method for the Laplace equation, [PDF]  [Some Correction] Methods and Applications of Analysis, v13 (2006), pp.215-233. (Special issue dedicated to Professor Bjorn Engquist on the occasion of his 60th birthday)
  
  
  • 4) F. Li and C.-W. Shu, Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations, [Abstract]  [PDF]  Applied Mathematics Letters, v18 (2005), pp.1204-1209.
  
  
  • 3) F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for MHD equations, [Abstract]  [PDF]  Journal of Scientific Computing, v22-23 (2005), pp.413-442.
  
  
  • 2) B. Cockburn, F. Li and C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for the Maxwell equations, [Abstract]  [PDF]  Journal of Computational Physics, v194 (2004), pp.588-610.
  
  
  • 1) L.-A. Ying and F. Li, Exterior Problem of the Darwin Model and its Numerical Computation, [Abstract]  [PDF]  Mathematical Modelling and Numerical Analysis, v37 (2003), pp.515-532.
  
  
• Publications in Conference and Workshop Proceedings
  
  
  • 4) S. C. Brenner, F. Li and L.-Y. Sung, Nonconforming Maxwell eigensolvers, Oberwolfach Report No. 36, 2008, the proceedings for the workshop "Nonstandard Finite Element Methods, Mathematisches Forschungsinstitut Oberwolfach, Germany, August 10-16, 2008, pp.42-43
  
  
  • 3) F. Li, C.-W. Shu, Y.-T. Zhang and H.-K. Zhao, A DGM-based fast sweeping method for Eikonal equations, Oberwolfach Report No. 36, 2008, the proceedings for the workshop "Nonstandard Finite Element Methods", Mathematisches Forschungsinstitut Oberwolfach, Germany, August 10-16, 2008, pp. 38
  
  
  • 2) S. C. Brenner, F. Li and L.-Y. Sung, A locally divergence-free nonconforming finite element method for the reduced time-harmonic Maxwell equations, [PDF]  Proceedings of the joint Workshop by AWM and MSRI: The Legacy of Ladyzhenskaya and Oleinik, 2006, pp.187-191.
  
  
  • 1) B. Cockburn, F. Li and C.-W. Shu, Discontinuous Galerkin methods for equations with divergence-free solutions: preliminary results, the proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, K.J. Bathe, Editor, June 2003, Elsevier Science, pp.1900-1902
  
  
• Unpublished
  
  
  • F. Li, A priori error estimates of a local-structure-preserving LDG method, [PDF], May 2011.